Limits of functions as x approaches infinity

As you compute limits of functions as x approaches a constant, you can find several possible solutions:

The limit is equal to a constant

The limit is plus or minus infinity

The limit does not exit

We have three rules for evaluating the limit of a rational expression as x approaches infinity:

If the highest power of x in a rational expression is in the numerator, then the limit as x approaches infinity is infinity.

If the highest power of x in a rational expression is in the denominator, then the limit as x approaches infinity is zero.

If the highest power of x in a rational expression is the same in both the numerator and denominator, then the limit as x approaches infinity is the coefficient of the highest term in the numerator divided by the coefficient of the highest term in the denominator.